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Every Boolean algebra is isomorphic to the Boolean algebra of sets. The theorem is equivalent to the maximal ideal theorem, which can be proved without using the axiom of ...

A C^*-algebra is a Banach algebra with an antiautomorphic involution * which satisfies (x^*)^* = x (1) x^*y^* = (yx)^* (2) x^*+y^* = (x+y)^* (3) (cx)^* = c^_x^*, (4) where ...

A Banach algebra A is called contractible if H^1(A,X)=Z^1(A,X)/B^1(A,X)=0 for all Banach A-bimodules X (Helemskii 1989, 1997). A C^*-algebra is contractible if and only if it ...

Ore algebra is an algebra of noncommutative polynomials representing linear operators for functional equations such as linear differential or difference equations. Ore ...

The conjecture that the equations for a Robbins algebra, commutativity, associativity, and the Robbins axiom !(!(x v y) v !(x v !y))=x, where !x denotes NOT and x v y denotes ...

A topological algebra is a pair (A,tau), where A=(A,(f_i^A)_(i in I)) is an algebra and each of the operations f_i^A is continuous in the product topology. Examples of ...

There are two types of singular values, one in the context of elliptic integrals, and the other in linear algebra. For a square matrix A, the square roots of the eigenvalues ...

Let L be a finite-dimensional split semisimple Lie algebra over a field of field characteristic 0, H a splitting Cartan subalgebra, and Lambda a weight of H in a ...

A complex manifold for which the exterior derivative of the fundamental form Omega associated with the given Hermitian metric vanishes, so dOmega=0. In other words, it is a ...

A quadratic equation is a second-order polynomial equation in a single variable x ax^2+bx+c=0, (1) with a!=0. Because it is a second-order polynomial equation, the ...